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Hydraulic Design of Energy Dissipators for Culverts and Channels
Hydraulic Engineering Circular Number 14, Third Edition

Appendix C: Structural Considerations For Roughness Elements

Blocks, sills, and other roughness elements are used to impose exaggerated resistance to flow and to force and stabilize the hydraulic jump. They may be employed inside the culvert barrel, at the culvert exit or in open channels. Roughness elements must be anchored sufficiently to withstand the drag forces on the elements. The fluid dynamic drag equation is:


FD = CD AF ρ Va2 /2


CD = coefficient of drag (The maximum CD for a structural angle or a rectangular block is 1.98 (Horner, 1965).)

ρ = density of water, 1000 kg/m3 (1.94 slugs/ft3)

Va = approach velocity acting on roughness element, m/s (ft/s)

The roughness elements in the CSU rigid boundary basin, the USBR basins, the SAF basin, and internal dissipators must be able to satisfactorily resist the drag force over the lifetime of the structure. The drag force may be assumed to act at the center of the roughness element as shown in Figure C.1.

Figure C.1. Forces Acting on a Roughness Element

Diagram showing the drag force, F sub D, acting horizontally and the response anchor force, F sub A acting vertically. Variables are defined with Equation C.2.

The anchor forces necessary to resist overturning can be computed as follows:


FA = hFD/2Lc = 0.5 (h/Lc) AFρVa2


FA = total force on anchors

FD = drag force on roughness element

h = height of roughness, m (ft)

LC = distance from downstream edge of roughness element to the centroid of the anchors, m (ft)

AF = frontal area of roughness element, m2 (ft2)

Va = approach velocity acting on roughness element, m/s (ft/s)

ρ = density of water, 1000 kg/m3 (1.94 slugs/ft3)

The approach velocity, Va, should be selected as a worst case using the approach velocity at the first row for Va. In cases of tumbling flow or increased resistance on steep slopes, use the normal velocity of the culvert without roughness elements for Va.

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Cynthia Nurmi
Resource Center (Atlanta)

Updated: 04/07/2011

United States Department of Transportation - Federal Highway Administration